Racing quads are fairly simple to build. The fundamental components are as follows:

Flight Controller: The brain of the quad.

Motors and Propellers

Electronic Speed Controllers

Power Distribution Board

Receiver

Battery

For this quad I chose the Naze32 flight controller, which is a fairly advanced flight controller that supports the Cleanflight software. My full parts list can be found here. This document also outlines all the tools required to build the machine from scratch.